And what has changed after Obama’s intervention is that the two sides are thinking harder than ever about strategy and positioning, with the clearest division yet between an argument about the economy or one on immigration.
The remain side have been accused of scaremongering, but after support from the International Monetary Fund and the Institute of Fiscal Studies, the publication of a weighty Treasury report and the backing of the leader of the free world, they will rightly feel on the front foot when it comes to the economy.
So what can the outers do? “We need to neutralise them on the economy,” says one source, meaning they talk about business, they rebut Obama and they question the Treasury figures. But they also accept that they cannot possibly win on the issue of finances.
Which is why this week’s fightback is not about the money, but immigration: about free movement, about the accession of Turkey and about the impact it all has on public services such as the NHS.
The message is of an EU deal in which the UK “puts in a lot of money and gets out lots of immigration”.
And as for the intervention of Obama, Hollande, business leaders and European diplomats? “It is a David v Goliath fight. We are up for that,” says Paul Stephenson, spokesman for Vote Leave. “The EU is good for people in power, including multinational corporations and world leaders. That doesn’t mean it is good for British people.”
Immigration shifted to top of EU referendum agenda by out campaigners
